# Is there a common mathematical symbology for collections?

Preface: So, it was suggested in 'Programmers' that I ask this over here.

I am being asked to define several of my algorithms in mathematical terms to describe my work to a customer. I trying to determine if anybody knows whether common operators for collections like sequences, lists, tuples, etc have been defined. If so, is there a good reference that I could be pointed to. Thanks. I am interested in the actual symbols used. I am wondering if the following would make sense or be appropiate to anybody.

Given two sequences (or strings):

S = (A, B, C) and T = (A, D, H)

In my mind, the intersection of these sequences would look like S ∩ T = (A) and the union of these sequences would be S ∪ T = (A, B, C, A, D, H)

• It's not clear what intersection and union look like for sets of sequences: your intersection operation looks like a set intersection, but the union operation looks like a disjoint union, and probably should merely be concatenation (+). Nov 17, 2010 at 23:27
• In my math education I have yet do encounter a notation for collections (or multisets). I would probably go with $[A, B, A, ...]$ because I am not aware of any conflicts and it is immediately clear to any programmer. Dec 18, 2010 at 9:35